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CoA R E P O R T AERO No. 208
'M HOGESCHOOL DELFI VtJÖGTUIGBOUWKUNDEBIBLIOTHEEK
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Kiuyverweg 1 - 2ö29 HS DELFT
THE COLLEGE OF AERONAUTICS
CRANFIELD
AN ANALOGUE SIMULATION OF THE LONGITUDINAL
MOTION OF A GROUND E F F E C T WING
by
CoA Report A e r o No. 21)8 November, 1968.
THE COLLEGE OF AERONAUTICS
CRANFIELD
An analogue s i m u l a t i o n of the longitudinal motion of a ground effect wing
by
p . E. K u m a r , B. Sc. (Eng), A. C. G. I.
SUMMARY
The longitudinal equations of motion of a G. E. W . , previously developed, w e r e u s e d on a 14 a m p l i f i e r analogue c o m p u t e r to s i m u l a t e the dynamic behaviour of the craft. Two pilots w e r e used for t h e s e t e s t s and the effect of varying the derivative mjj w a s investigated. This simulation was useful qualitatively only and it was con-cluded that a fuller simulation i n c o r p o r a t i n g n o n - l i n e a r d e r i v a t i v e s would be of g r e a t e r u s e on a quantitative b a s i s . T h i s would have to be done on a much l a r g e r analogue c o m p u t e r such a s the AD 256 of the E l e c t r i c a l D e p a r t m e n t .
CONTENTS Page S u m m a r y Symbols Introduction 1 Equations of motion 1 Analogue s i m u l a t i o n 2 R e s u l t s 2 Conclusions 2 R e f e r e n c e s 3
SYMBOLS
c m e a n wing chord
h height of wing above ground r e l a t i v e to s o m e datum point on wing e. g. q u a r t e r chord.
u , w p e r t u r b a t i o n v e l o c i t i e s along x and z wind a x e s . u, w p e r t u r b a t i o n a c c l e r a t i o n s along x and z wind a x e s .
h r a t e of change of height ( a s s o c i a t e d with ground shape) q p e r t u r b e d r a t e of pitch A A ^ I I I u , w, h e t c . n o n - d i m e n s i o n a l p e r t u r b a t i o n s u/Vo» w/Vo. h / c e t c . Vo free s t r e a m velocity t m/pSVo m m a s s of craft S craft plan a r e a ^ h ' ^ . ^q. "'^w n o n - d i m e n s i o n a l a e r o d y n a m i c d e r i v a t i v e s . e t c . ^\ r e l a t i v e density p a r a m e t e r m / n g i j . *^2 r e l a t i v e density p a r a m e t e r TCij^So Ij. moment a r m of t a n d e m wing i-g n o n - d i m e n s i o n a l pitching i n e r t i a . e p e r t u r b a t i o n in incidence of craft
1
-Introduction
The longitudinal dynamic stability of a G. E. W. (ground effect wing) was in-v e s t i g a t e d in ref. 1 w h e r e the l i n e a r i s e d equations of motion w e r e deriin-ved, A v e r y brief analogue s i m u l a t i o n of a single wing with endplates and a tandem-wing configuration had been undertaken and the p r e s e n t note c a r r i e s the work f u r t h e r . A t a n d e m - w i n g configuration h a s once again been used with l i n e a r i s e d d e r i v a t i v e s taken at a fixed height above ground. No v a r i a t i o n of the d e r i v a t i v e s with changes in height from the d a t u m w e r e allowed for at t h i s s t a g e , a s only a fourteen
a m p l i f i e r analogue c o m p u t e r was u s e d , and the r e s u l t s a r e , t h e r e f o r e , useful qualitatively only. The d e r i v a t i v e s u s e d w e r e obtained from the wind-tunnel t e s t s of ref. 2,
Equations of motion
The full equations of longitudinal motion a r e given in ref. 1. However, for the p r e s e n t work the equations have been used in t e r m s of r e a l t i m e , a s opposed to a e r o d y n a m i c t i m e , and a r e a s follows:
du = l(uxu + wx^+hxjj-CLej-i-xi{ dli
"ar
f
~2~ ~2 dt"
, A /\ dw_ = l ( u z y + w z ^ + h z j ^ - C L t a n e e ) + (1+z^) de + zjj dh dt T ~ 2 ~ /u^ dT T r ^ l T ^^' 2 » A . A ** A —A d e = m(mvy dw +mh dh) + mq dd + ^ i { u m y + w m w + c h m h +m^ 'n-i) dt2 i s i dt M2 dt i-^ dt i"B^2 ï ^ A '* A /:/ w + 1 d h = Q dtThe l a s t r e l a t i o n of equations (1) is m e r e l y a boundary condition indicating that the craft is flying over level ground. The d e r i v a t i v e s used a r e b a s i c a l l y those u s e d i n section 4 . 3 of ref. 1, with the addition of an e l e v a t o r , o r r e a r wing, c o n t r o l d e r i v a t i v e m . T h e s e d e r i v a t i v e s for the G. E. W. model a r e :
-9. 54. ^ 2
e =
a t V Xu = Xw = Xh = C L 2 8° o - . 0. 0 = 0 . I r = L 9 5 5 , = 4 0 f t / s e c , iJ-i 016 614 016 75 Zu = Zw = Zh= (i+za)= H i B = = - 1 . - 5 - 0 . 0. 9. 49 68 75 7 = l O l b s , = 18. m u ~ m w = m h = m q = 5, 0 - 2 . - 0 . - 2 t = h = 68 175 845 1. 2 37 . 0 " s e e s "Hi = - 2 . 8 4 5F o r lack of information at the p r e s e n t t i m e the following d e r i v a t i v e s have b e e n t a k e n a s z e r o !
Analogue simulation
The block d i a g r a m of the analogue c i r c u i t can be s e e n in Fig. 1. The e l e v a t o r input ,^im^Ti.|v was p r o p o r t i o n a l to a p o t e n t i o m e t e r output r e s i s t a n c e controlled d i r e c t l y
iBt by the 'pilot'.
The r u n s on the s i m u l a t o r w e r e done stick fixed, to obtain the r e s p o n s e of the craft to an e l e v a t o r d i s t u r b a n c e , and then 'flown' by the pilot by monitoring the height above ground p a r a m e t e r displayed on an o s c i l l o s c o p e . The pilot attempted to m i n i m i s e his d e p a r t u r e s from the datum height. Runs w e r e done with v a r i o u s values of mji ranging from negative through z e r o to positive.
Recordings of the v a r i a t i o n of e l e v a t o r angle .^i incidence and height above (or below, ) ground h, with t i m e w e r e made on a U-V r e c o r d e r and s o m e of t h e s e t i m e h i s t o r i e s a r e shown in F i g s 2(a) — 4(c).
Two pilots w e r e used in this simulation to give a b e t t e r indication a s to the controllability of the craft.
R e s u l t s
As has been pointed out previously the r e s u l t s shown in F i g s . 2 _ 4 a r e of a qualitative n a t u r e . The G. E. W. has been allowed to move below the initial datum height which, u n d e r p r a c t i c a l conditions, would have m e a n t contact with the ground.
It can be seen that the r e s p o n s e s in 6 and h due to initial e l e v a t o r d i s t u r b a n c e s change from a divergent o s c i l l a t o r y mode to a divergence a s ra-u v a r i e s from negative to positive v a l u e s . The controllability of the craft is best for negative mj^ with s m a l l c o n t r o l m o v e m e n t s n e c e s s a r y to k e e p the d e p a r t u r e s in height s m a l l . This again holds t r u e for positive m ^ but to a l e s s e r extent. However, the indications for both these c a s e s a r e that the oscillations in 6 and h a r e becoming divergent. F o r mj^ = 0 the motion is p r a c t i c a l l y uncontrollable. All oscillations a r e v e r y r a p i d l y divergent inspite of l a r g e c o r r e c t i v e control m o v e m e n t s .
The limitations on the p r e s e n t simulation a r i s e from
(a) No v a r i a t i o n of the d e r i v a t i v e s with height a n d / o r incidence.
(b) The u s e of a p o t e n t i o m e t e r control, a s opposed to a ' s t i c k ' which has been shown to give quicker r e s p o n s e s from pilots flying s i m u l a t o r s .
Conclusions
The simplified analogue simulation has confirmed that the derivative mj^ i. e. v a r i a t i o n of pitching moment with height, is of vital i m p o r t a n c e in the longitudinal dynamic r e s p o n s e of a G, E. W. Negative v a l u e s of mh produce o s c i l l a t o r y (and divergent) stick fixed r e s p o n s e s to d i s t u r b a n c e s but give r e a s o n a b l e c o n t r o l of the craft when being flown. Positive mh gives a divergent stick fixed r e s p o n s e to a d i s t u r b a n c e , but also y i e l d s a controllable craft. Z e r o mh a p p e a r s to be the w o r s t c a s e c r e a t i n g an uncontrollable craft although it gives s m a l l d e p a r t u r e s from the datum in the stick fixed disturbed c a s e . This is r a t h e r unexpected and
3
-In conclusion i t i s s u g g e s t e d that a fuller simulation including the non-l i n e a r t e r m s of the d e r i v a t i v e s be done on a non-l a r g e r ananon-logue c o m p u t e r , such a s the AD 256 of the CoA. E l e c t r i c a l D e p a r t m e n t , to give a m o r e complete
a p p r e c i a t i o n of the stability p r o b l e m s involved in G. E . W . ' s .
R e f e r e n c e s
1. P . E. K u m a r On the longitudinal dynamic stability of a ground effect wing.
CoA r e p o r t A e r o 202 (1968)
2. P . E. K u m a r An e x p e r i m e n t a l investigation into the A e r o -dynamic c h a r a c t e r i s t i c s of a wing, with and without endplates, in ground effect.
FIG.I. ANALOGUE REPRESENTATION OF THE
LONGITUDINAL EQUATIONS OF MOTION
(t>)
FIG. 2/»H'EFFECT OF LENGTH OF ELEVATOR DISTURBANCE ON ENSUING M O T l O N
OF G.E.W. ( m , _ 0 )
FIG.2 ( c l . TIME HISTORIES FLIGHT PATH - PILOT'A' ( m , . 0 )
FIG. 2(dl TIME HISTORIES FLIGHT PATH PILOT B
